QUANTIFYING THE INFLUENCE OF TOPOGRAPHIC-MODEL-RELATED DISTORTIONS ONCRATERING CHRONOLOGIES A. Neesemann1, S. van Gasselt2, R. Jaumann3 1Freie Universität Berlin, Inst. ofGeological Sciences, Planetary Sciences and Remote Sensing Group, Malteserstr. 74-100, 12249 Berlin, (Germany);adrian.neesemann@fu-berlin.de; 2Dept. of Geoinformatics, University of Seoul, South Korea; 3German AerospaceCenter (DLR), Inst. of Planetary Research, Berlin, Germany

Figure 1: Deviation of heights between used reference ellipsoids. Here we expressed the deviation in the form of the areal correction factor xa ascolor-coded, semi-transparent images superposed on hillshade models of the respective body. We demonstrate the effect for the most commonlyused global DEMs converted to elevations above or below the corresponding reference ellipsoid. Mars: MOLA MEGDR - 3396 km sphere [20,21]; Moon: LRO LOLA LDEM GDR - 1737.4 km sphere [21, 22]; Ceres: Dawn FC HAMO DTM - 470 km sphere [23]; Vesta: Dawn FC HAMODTM - 255 km sphere [24]. The percentage of distortion Da is given by

√((xa − 1) · 100)2 accordingly. During the projection, reddish regions

will be down-sized while bluish regions will be scaled-up. Black solid lines show the course of the 0-m isohypses or intersection lines between thereference sphere and the actual shape of the bodies. Only here, the topography related distortions are zero (xa = 1).

Introduction: Analyzing crater densities and cratersize-frequency distributions (CSFDs) is an establishedapproach for dating planetary surfaces that cannot bedirectly linked to radiometrically dated rock samples[1-6]. Like in many scientific approaches, the accu-racy of crater-based age dating also depends on a num-ber of systematic errors. Imperfect calibration of em-pirically derived or modeled chronology systems (CSs)can be considered as the primary error sources. Whilethe attempt to quantify such errors is challenging, sec-ondary issues of statistical [7-10] and metrological [11]nature that influence the outcome of crater-based agedating were already addressed and basically solved inthe past. Other influences, such as the inherent variabil-ity of crater identification among crater analysts [12] or

the influence of secondary crater admixture [i.a. 13-18]were illustrated at great detail but are still under discus-sion.

Here we introduce another issue of metrological ac-curacy which, under certain conditions, can have an ap-preciable impact on measured crater diameters and areasize and thus on the derived absolute model ages.

Background: In Geodesy, accurate distance or areacalculations can be challenging as the real shape of aplanetary body is often irregular. Instead, due to theirrelative simplicity, reference ellipsoids are used as a pre-ferred surface on which geodetic calculations are per-formed. They generally constitute a close approxima-tion to the true figure of large objects with low relief-to-size ratios, such as the terrestrial planets or large Jo-

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Figure 2: Relative crater frequency [5] of a hypothetical 1 Ma and 4.5 Ga measurement on a 255 km sphere for CSs of [28] (left) and [29, 30](center) and on a 3396 km sphere for the CS of [26, 27] (right). Note that the impact on model ages is almost identical for ages below ~3 Gabetween the two Vestan systems since chronology functions of [28] and [30] are also almost identical within that time interval.

vian and Saturnian moons. Especially for the well ob-served and most frequently investigated bodies such asthe Earth, the Moon, and Mars, quite precise referenceellipsoids exist [e.g. World Geodetic System (WGS84),19, 20] which are commonly used and already satisfac-tory for most purposes. While on the Earth a numberof localized geodetic datums are available which cangive a more accurate representation of the region of in-terest, it is customary in planetary science to maintainglobally representative reference ellipsoids. As a conse-quence, remote sensing data on which we perform mea-surements become distorted depending on the local dif-ference between the actual shape of the body and theapplied reference ellipsoid (fig. 1).

In principle, correcting the projection distortions is,from a mathematical point of view, relatively simple.Linear (crater diameter) errors are proportional to the ra-tio of the radii of the actual shape to the reference ellip-soid while areal errors are proportional to their squaredratio. But how can the resulting ratios be translated intomodel age variation?

Methodology: Here we quantify and evaluate theseeffects directly on CSs proposed for four planetary bod-ies. The Moon and Mars were chosen to demonstratethe aforementioned effects on the most frequently in-vestigated bodies in terms of crater-based age determi-nation. Additionally, due to their relatively low relief-to-reference-ellipsoid-size ratio (Mars ~0.6%, Moon~0.6%) they constitute as something like end members(both are in hydrostatic equilibrium and have thereforea round shape) on which topography related distortionscan almost be considered negligible. For demonstrationpurposes, we used the still most widely used CS of [25]for the Moon, and [26, 27] for Mars. At the other end ofthe relief-to-size ratio scale we have asteroid Vesta anddwarf planet Ceres (fig. 1) with high relief-to-size ratios(16.9%, 5.9%).

Results: In fig. 2, we show the impacts on twochronologies proposed for Vesta [28-30] for two scenar-ios: A hypothetical measurement of a 1 Ma and a 4.5 Gaold surface on a 255 km reference sphere. If the hypo-thetical measurements were performed in high (VestaliaTerra) or low (Rheasilvia basin) regions, then CSFDsand related model ages would change as shown.

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Acknowledgements: This work was partly supportedby the German Aerospace Center (DLR) on behalf of the Fed-eral Ministry of Economic Affairs and Energy, grant 50 OW1101.

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